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Prof. J. C. Maxwell on Electric Induction. [Feb. 15, 



illness, we, with heartfelt thankfulness, rejoice with Your Majesty 

 and all Your Majesty's subjects throughout the Empire in His Royal 

 Highness's happy recovery. That he may long be spared to Your 

 Majesty, to his Family, and to the People of this Country, is the earnest 

 wish and prayer of Your Majesty's loyal and devoted subjects, the Pre- 

 sident, Council, and Fellows of the Royal Society of London." 



On the motion of Mr. C. B. Vignoles, seconded by Dr. Webster, it was 

 resolved that the Fellows do most cordially concur in the Address now read 

 from the Chair. 



The Address was then signed by the President on behalf of the Council 

 and Fellows. 



The following communications were read : — 



I. " On the Induction of Electric Currents in an Infinite Plane 

 Sheet of uniform conductivity." By Prof. J. Clerk Maxwell, 

 E.R.S. Received January 10, 1872. 



1. When, on account of the motion or the change of strength of any 

 magnet or electromagnet, a change takes place in the magnetic field, elec- 

 tromotive forces are called into play, and, if the material in which they 

 act is a conductor, electric currents are produced. This is the phenomenon 

 of the induction of electric currents, discovered by Faraday. 



I propose to investigate the case in which the conducting substance is in 

 the form of a thin stratum or sheet, bounded by parallel planes, and of 

 indefinite extent. A system of magnets or electromagnets is supposed to 

 exist on the positive side of this sheet, and to vary in any way by changing 

 its position or its intensity. We have to determine the nature of the cur- 

 rents induced in the sheet, and their magnetic effect at any point, and, in 

 particular, their reaction on the electromagnetic system which gave rise to 

 them. The induced currents are due, partly to the direct action of the 

 external system, and partly to their mutual inductive action ; so that the 

 problem appears, at first sight, somewhat difficult. 



2, The result of the investigation, however, may be presented in a re- 

 markably simple form, by the aid of the principle of images which was 

 first applied to problems in electricity and hydrokinetics by Sir W. Thomson. 

 The essential part of this principle is, that we conceive the state of things 

 on the positive side of a certain closed or infinite surface (which is really 

 caused by actions having their seat on that surface) to be due to an ima- 

 ginary system on the negative side of the surface, which, if it existed, and 

 if the action of the surface were abolished, would give rise to the actual 

 state of things in the space on the positive side of the surface. 



The state of things on the positive side of the surface is expressed by a 

 mathematical function, which is different in form from that which ex- 

 presses the state of things on the negative side, but which is identical with 



